Discussion of Round #6

At daybreak, all remaining players will be blindfolded and have hats placed upon their heads. The hats will be either black or white.

Each player will be selected, one at a time. That player's blindfold will be removed so that he can see all the other hats. Using just this information, he will attempt to guess the colour of his own hat. He may only say "black" or "white". If the player successfully guesses the colour of his hat, he will earn the right to vote. If he is incorrect, he will not earn the right to vote, and will be shot! Then, the next player will have his turn to guess.

You have the night to discuss your strategy.

Obviously, there are only two possible answers, so each player will have only one chance to answer correctly. Also, all players must submit their guesses before I will respond or announce who has earned the right to vote.

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At daybreak, the ten survivors discover the body of debc1, who was human . They realize that one wolf and the seer remain in the game.

Then, they proceed to the challenge area. Blindfolds are secured, and each player feels the soft plop of a hat landing on his or her head.

The Scapegoat, LanceKolaski, is selected to go first.

As soon as his blindfold is removed, Lance rolls his eyes upward to look at the brim of his hat. Then he looks to the moderator in confusion, because the brim of his hat appears to be gray. The moderator smiles and says, "Nice try, but it won't work. All hats have a silver lining. Proceed!"

After looking at the nine other hats, Lance says, "BLACK." He then reaches up and grabs his hat, to see if he is right. It is white. Lance walks over to face the firing squad.

Lance, please cast your vote for yourself now. If you earn - or are extended - the right to vote, you may change it. Other players are not allowed to vote for Lance until/unless he is able to change his vote!

WittyKitty is selected next. She looks at the eight remaining hats and says, "BLACK." She then doffs her hat, which is indeed black, with a silver lining.

Now, it is Limerick's turn. He looks at the seven remaining hats. He sees that KRUGERGIRL and mocha are wearing white hats, while the other five players are wearing black hats.

In order to earn the right to vote, tell me - what colour hat should Limerick say he is wearing? More importantly - why?

If players want to end the round early, you may vote to shoot the Scapegoat.

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---This message was edited on 2013-08-05 05:35:59---Ally or die. That is the motto of the new, REVAMPED version of Alliances I currently have. Alliances is a social game to the style of WWG and WTB. To learn more and/or play, PM me or check the public talkboxes. Come for a fun game!

But seriously, why not?Ally or die. That is the motto of the new, REVAMPED version of Alliances I currently have. Alliances is a social game to the style of WWG and WTB. To learn more and/or play, PM me or check the public talkboxes. Come for a fun game!

I have to admit, I am rather confused, haha, so are we not all guessing the colour of our own hats then are they all guessing mine? Or is this part only for me? And I thought you weren't revealing results until receiving all answers? Has Witty actually guessed and received the right to vote so far? Has Lance really actually guessed and being shot?

Limerick, that's the riddle for this round. Everyone has to guess what color your hat is.

EDIT: So, if I'm recalling correctly, Mocha, Yuffie, and buu are the only remaining suspects. One of them is a wolf. I'm leaning towards Yuffie being human, but I am unsure of Mochs and buu. Then again, the seer has had two rounds to divine people, so assuming they didn't divine me or kmr, they should've had the chance to divine two of the three.

Not much luck so far on the puzzle for this round. Also, I work a 10-hour shift today, so I won't be around much. However, I should be around some late tonight and tomorrow afternoon.

Idea! There are five teams left in the game, right? Is it possible for two of the teams to guess (one white, one black) and then let the other teams know? Because the answers to the puzzles have been given before in-game, but I was thinking maybe because this is a 50/50 chance round, that wouldn't be allowed. But if it is, we should totally utilize it.Baila como si nadie estÃ¡ mirando.

Oh, now I get the riddle! We're supposed to say what hat Lim is wearing, not our hat! Because that's the question!

Easy - one person PMs white' the other PMs black, and reveal the answer. Then we all recieve the right to vote and attack on buu!Ally or die. That is the motto of the new, REVAMPED version of Alliances I currently have. Alliances is a social game to the style of WWG and WTB. To learn more and/or play, PM me or check the public talkboxes. Come for a fun game!

Obviously, there are only two possible answers, so each player will have only one chance to answer correctly. Also, all players must submit their guesses before I will respond or announce who has earned the right to vote.

I feel some people are waiting to hear back on how Giz responds, but I don't think she is going to. I sent in my guess 6 hours ago and have yet to hear back. Then again, she also hasn't responded to my question here in game, so it could just be that she is busy, but she has been so good at getting back to us on the right to vote, I doubt it is that."Wir mÃ¼ssen wissen, und wir werden wissen." -David Hilbert

Well, since I really don't know what can be done with this with my thoughts so far... here is what I have from my talk box:

This puzzle has two classic solutions both of which the first person has a 50/50 chance of guessing correctly and everyone else can guess correctly.

1) First guesser guesses the color he sees an odd number of, from there people compare what they are seeing to solve. This teaser is an example of this solution.

2) First guesser guesses the color he sees an even number of, from there people compare what they are seeing to solve.

Two possible starting points exist for this particular instance of the puzzle, Lance sees: 6B, 3W or 7B, 2W (What I see plus Witty's black plus whatever I am wearing)

Assuming the first strategy is at play here, we are dealing with 7/2, Lance guesses Black since he sees an odd number of black, Witty sees 6/2, knows Lance saw an odd number of black, since she is seeing an even, knows her hat is black and guesses Black. I, knowing Lance saw an odd number of black, know Witty's was black making my count 6/2, know mine must be black... etc...

Assuming the second strategy is at play here, we are dealing with 6/3, Lance guesses Black since he sees an even number of Black, Witty sees 5/3, knows Black was even for Lance and is now odd so, knows her hat is Black, I see 5/2, know that Lance saw an even number of black, know Witty's was black making my count 6/2 which is still even, so I know mine is white and guess White...

From the standard constructs, there is not enough information to solve this since we don't know if Lance was using the even or odd strategy... So there has to be more.

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And there is indeed white text here, which may be a hint in and of itself, but, heh....

Right now, I have to believe there is a definitive answer to this... but the solutions above are widely recognised to be the only definitive answer to this extremely well studied problem. So, I have to believe there is some way to determine which parity (odd or even) is being used.

As far as being a 50/50 challenge...

In order to earn the right to vote, tell me - what colour hat should Limerick say he is wearing? More importantly - why?

Depending on how you read this, she may not accept an answer if you can't explain it, though, I don't know if this is true or not as that part is in white and might not really technically be part of the challenge...

Well, honestly, the one thing I want to make sure of is that we get at least 2 people (other than buu) with each color vote. That is all that really matters. We don't all need the right to vote. People who have voted should put their votes in white text with spoiler tags so we can make sure to wrap this up. Not that I am toooooo concerned we will have everyone get them wrong, but, you know :p

If Gizzer enforces us shooting everyone who gets it wrong, we could already be really close to losing the game though... So, we also want to be careful. I would be in favor of limiting much in the way of further votes.

I have heard from all but one player, either through the game, in the talkboxes, or by PM. Due to rule infractions, this player cannot earn the right to vote, so I will end the challenge now and provide the solution.

Round 6 ChallengeBlack or White

In order to earn the right to vote, tell me - what colour hat should Limerick say he is wearing? More importantly - why?

Solution:

BLACK

There are many logic teasers on Braingle about determining the colour of hats. This one is based on Survival of the People. In the teaser, the first player guesses BLACK if he sees an ODD number of black hats, or WHITE if he sees an ODD number of white hats. So, the Scapegoat's guess of BLACK indicates that he can see an odd number of black hats. The fact that his hat is actually white is irrelevant. The next person's hat was black, so there would now be an even number of black hats. Since Limerick can see an odd number of black hats, his hat must be BLACK.

The real challenge was that you also had to follow the instructions:

1) Teams could strategize during the night only. This limited strategizing to the talkboxes. Giving the answer or telling people how to vote within the game would result in forfeiture of the right to vote.

2) Once the challenge began, players could only say BLACK or WHITE in the game until the challenge was over. The lack of any other communication between participants during the test is fundamental to this kind of puzzle. I did not post in the game until the challenge was over so as not to encourage discussion! By saying BLACK or WHITE, each player could indicate what their guess would be in the game, and then send me the reason by PM. The last players to guess could therefore ensure that both answers were adequately represented. Indeed, if everyone had simply given the colour of their own hat - which was provided for everyone except Limerick - enough humans could have earned the right to vote to end the game in this round.

3) If the previous rules had been followed, the silver lining for the wolves was that all players had to guess. This, of course, included the wolf, who could thwart the humans' plans simply by saying they refused to guess. Passively not guessing would be considered insufficient, and would not preclude the humans from earning the right to vote.

The challenge, therefore, would run until: a) time ran out; b) all/enough guesses were received or c) all/enough players lost the right to vote - whichever came first.

Of the remaining players, only one earned the right to vote.

I'll now respond to the private messages and post in the team talkboxes.

I will not comment on who earned the right to vote, but I will say that the rules of the game prevent that player from extending the right to vote to anyone else.

Therefore, there will be no more than 2 people voting, which means the round will time out. As those on Lance's team can confirm, Lance will not be allowed to change his vote. The player who earned the right to vote can, at best, create a tie. The computer would then decide who is shot.

Before I get jumped on for not extending the right to vote, to do so means I had to share it with my team first, and I figured it was best to keep it out of the hands of the wolf. I thought with a 50% chance of getting it right we were not in danger of not getting enough votes!

I know it means waiting and possibly going another round, but I'm all for letting us have a 50% chance of getting buu shot. Better than 100% chance of shooting lance, I think."Wir mÃ¼ssen wissen, und wir werden wissen." -David Hilbert

Man am I confused; I was not aware there were rules I correctly found the right teaser but I second-guessed myself (with the Odd/Even thing) & got it wrong anyway - should've just gone with my personal choice of black >.<

Mocha did what she thought was right & as her fellow teammate, I support her decision ^_^ But hypothetically, could she have extended it to us or did I break the rules (I can't recall when I wrote in the talkbox )? If she & I voted for Buu, then Buu could only vote alongside Lance (to create a tie) but if she won it for our team, we could've extended it to Team Bravo, right? Or did they break the rules as well?

Eh, either way - we know who the final wolf is, so this round wasn't wasted; unless no one is able to answer the rest of Gizzer's challenges (which I don't think will be the case) humans will win the game - it's just a matter of time

As far as us voting for Lance just to end the round - I say we leave it up to the game, as we'll have more of a chance at ending it than if we just hurried along, ya know? (Also b/c I'm not going to be on much today anyway so having the round time out really isn't a big deal LOL)

Yuffie, you are totally right, and I clearly didn't think. I was just focused on not giving buu the RTV, not thinking that I could have given it to more humans who would have shot him. Again, I made the decision back when I figured 50% of us would have the RTV. I included in my pm with my answer that I didn't want to extend it to my team. So that had nothing to do with breaking rules or anything."Wir mÃ¼ssen wissen, und wir werden wissen." -David Hilbert

Actually, I can at least tell you it is not alphabetical. As you can see in this game. Here Smithy and Rhythmic, both human were tied, Smithy was shot. This one however is alphabetical, so it is not reverse order.

As far as saving the wolves, a possible example. Another.This one proves that wolves CAN be shot in ties however, so any favoritism is not 100%.

At this point, I would have to say personally I am on the side of saying it is random. But, who knows how the actual calculation is done, there could be some favoritism =p

ETA: I noticed in the Caberet/Koin example of a wolf being shot out of a tie, Cab was the Seer, so to rule out that having been the reason a wolf got shot, here is an example of a wolf/human tie. No time now to look for another Seer/Wolf tie to see if the Seer might not be favoured though =p